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Train keeps a rollin’ indeed. No matter how battered or broken Aerosmith has appeared to be over the past couple of years, the band soared through a 90-minute homecoming Tuesday at the TD Garden.

Aerosmith and openers Cheap Trick sold out the Garden, and both return Thursday for ­another show. Tickets are still available.

At first it seemed the acrimony that built up when singer Steven Tyler joined the cast of “American Idol” lingered. After Tyler and guitarist Joe Perry emerged together from the end of a ramp extending from the main stage for the raucous opening number “Draw the Line,” the singer spent much of his time orbiting his bandmates.

But then Tyler did huddle with the crew when Aerosmith dove into the slinky new “Oh, Yeah.” It was here you could see all of the members working together, feeling their collective way through something that 40-odd years of ­reflexive muscle would not know.

From there, whenever Tyler took off for his flights of fancy, it seemed simply that he trusts the guys behind him. And those guys trust him to be a fireball fully committed to the job of selling Aerosmith.

Everything balanced out just right. The show, while tightly choreographed around visual pizzazz, never stifled the raunchy charm of the music. Whitford and Perry let loose throughout the night, and Kramer got a lengthy solo break.

The set list favored the band’s more rocking side, with the evening’s highs clustering around ’70s gems “Last Child” and “No More, No More.” Latter-day Aerosmith was served up early with a run through “Living on the Edge,” “Cryin’,’’ and “Jaded,” all still better choices than the power ballad “I Don’t Want to Miss a Thing,” a big hit omitted.

Closing with the primal grit of “Train Kept ­a Rollin” was as simple a retort to Tyler’s tenure on “American Idol” as anyone needs.

Cheap Trick, a classic band in its own right, delivered an hourlong opening set of beautifully crafted, frenetically played power pop.